Self-Organization of Plutonomy in a Fair Competitive Society

We investigate the origin of the emergence of the plutonomy, an extreme form of hierarchy, where the top 1% of households account for more wealth than the bottom 99%. For a model fair society where individuals participate in a competition with equal right, we show that the plutonomy can be self-organized when individuals divided into several groups compete with those in the same group for a certain period (season) and they are regrouped at the end of every season. In the fair society, the wealth flows steadily from lower groups to the highest group, which is the origin of the plutonomy. Using mean-field analysis, we show that the fraction of winners decreases in proportion to the inverse of the number of groups.